For an exhaustive description of the discretisation schemes and numerical framework employed for solving the above mentioned governing equations, we refer the reader to [1]}, [2]}, and to [3]} for a comprehensive account of the hybrid front-tracking/level-set method, also called Level Contour Reconstruction Method (LCRM). Here, we present a short summary of the most relevant aspects. The LCRM considers the combination of a fixed structured Eulerian grid for the resolution of field equations and a moving and deforming Lagrangian grid for the interface, discretised via an unstructured triangular mesh. These interface elements are consequently advected through the integration of the Lagrangian equation \(\text{d} \textbf {x}_{f}/\text{d}t = \textbf {v}\) , where \(\textbf {v}\)  corresponds to the interface velocity, which is interpolated from the Eulerian grid. This integration is carried out with a second-order Runge-Kutta method. The spatial derivatives of the fields in the Eulerian grid are discretised through a standard cell-centred scheme for all terms, with the exception of the non-linear convective terms, for which a second-order
essentially non-oscillatory (ENO) procedure is used [4]}, [5]}. For the viscous term in the momentum equation, a second-order centred difference scheme is employed. With regard to the temporal terms, a second-order Gear method [6]} is adopted with an implicit time integration for the viscous terms. The time step is set to be adaptive, according to the following criterion: \(\Delta t = \min \lbrace \Delta t_{\rm {cap}}, \Delta t_{\rm {vis}}, \Delta t_{\rm {CFL}}, \Delta t_{\rm {int}}\rbrace \) , where the time steps relate to viscosity, capillarity, Courant-Friedrichs-Lewy condition, and interface, respectively. The time-step related to the interface was found to be the limiting time-step in all of our simulations (\(\Delta t_{\rm {int}} \sim \)  O(\(10^{-7}\) )s).
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